LinearRegression.py

#-*- coding: utf-8 -*-
import numpy as np
from helpers import *

def linearRegression(alpha=0.01,num_iters=10):
    print("加载数据...\n")
    
    data = loadtxtAndcsv_data("data.txt",",",np.float64)  #读取数据
    X = data[:,0:-1]      # X对应0到倒数第2列 ，切片操作返回的是view，不占用额外的内存，但也不是numpy.ndarray类型                
    y = data[:,-1]        # y对应最后一列  
    num_samples = len(y)            # 总的数据条数
    num_col = data.shape[1]      # data的列数
    
    print("归一化特征...\n")
    X,mu,sigma = featureNormaliza(X)    # 归一化
    plot_X1_X2(X)         # 画图看一下归一化效果
    
    X = np.hstack((np.ones((num_samples,1)),X))    # 在X前加一列1，为了和w^ = [w b] 相匹配   
    theta = np.zeros((num_col,1))
    y = y.reshape(-1,1)   #将行向量转化为列

    print("执行梯度下降算法....\n")
    theta,J_history = gradientDescent(X, y, theta, alpha, num_iters)
    
    plotJ(J_history, num_iters)
    
    return mu,sigma,theta   #返回均值mu,标准差sigma,和学习的结果theta

# 标准化数值
def featureNormaliza(X):
    X_norm = np.array(X)            # 避免篡改原始数据

    # 计算每个特征的平均值和方差
    mu = np.zeros((1,X.shape[1]))   
    sigma = np.zeros((1,X.shape[1]))
    mu = np.mean(X_norm,0)          # 求每一列的平均值（0指定为列，1代表行）
    sigma = np.std(X_norm,0)        # 求每一列的标准差

    for i in range(X.shape[1]):     # 遍历列
        X_norm[:,i] = (X_norm[:,i]-mu[i])/sigma[i]  # 标准化，区别于归一化
    
    return X_norm,mu,sigma

# 梯度下降算法
def gradientDescent(X,y,theta,alpha,num_iters):
    # m = len(y)      
    n = len(theta)
    
    temp = np.matrix(np.zeros((n,num_iters)))   # 暂存每次迭代计算的theta，转化为矩阵形式
    J_history = np.zeros((num_iters,1))         # 记录每次迭代计算的代价值
    
    for i in range(num_iters):  # 遍历迭代次数    
        h = np.dot(X,theta)     # 计算内积，matrix可以直接乘
        temp[:,i] = theta - ((alpha)*(np.dot(np.transpose(X),h-y)))   # 梯度的计算，取决于损失函数
        theta = temp[:,i]
        J_history[i] = computerCost(X,y,theta)      #调用计算代价函数
        print('.', end=' ')      
    return theta,J_history  

# 计算代价函数
def computerCost(X,y,theta):
    # m = len(y)
    J = 0
    
    J = (np.transpose(X@theta-y))@(X@theta-y)/2 # 平方误差和作为loss函数
    return J
    
# 测试学习效果（预测）
def predict(mu,sigma,theta):
    result = 0
    # 注意归一化
    predict = np.array([852,2])
    norm_predict = (predict-mu)/sigma
    final_predict = np.hstack((np.ones((1)),norm_predict))
    
    result = np.dot(final_predict,theta)    # 预测结果
    return result
    
# 测试linearRegression函数
def testLinearRegression():
    mu,sigma,theta = linearRegression(0.001,100)
    print(f"\n计算的theta值为：{theta}\n")
    print(f"\n预测结果为：{predict(mu, sigma, theta)}\n")
    
if __name__ == "__main__":
    testLinearRegression()